We provide a first principles derivation of the microscopic entropy of a very general class of supersymmetric, rotating, and accelerating black holes in <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math>. This is achieved by analyzing the large-<math><mi>N</mi></math> limit of the spindle index and completes the construction of the first example of a holographic duality involving supersymmetric field theories defined on orbifolds with conical singularities.

Italy

Edoardo Colombo

United Kingdom

Seyed Morteza Hosseini

Dario Martelli

Antonio Pittelli

Alberto Zaffaroni

Microstates of Accelerating and Supersymmetric <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> Black Holes from the Spindle Index

We reassess the problem of symmetry restoration induced by observers’ acceleration within the context of interacting quantum field theories in Minkowski spacetime. We argue that the imposition of a frame-independent renormalization condition negates any observed symmetry restoration by a Rindler observer. Technically, we compute the one-loop effective potential of a λφ 4 theory for an accelerated observer, employing a distinct methodology from prior investigations. Emphasizing the intricacies of the model’s renormalization, the analysis offers novel insights into the interplay between acceleration and spontaneous symmetry breaking in quantum field theory.

Domenico Salluce

Japan

Marco Pasini

Antonino Flachi

Stefano Ansoldi

Symmetry restoration and uniformly accelerated observers in Minkowski spacetime

We find a one-dimensional protected subsector of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S 3. Then, we apply it to the novel case of S 2 × S 1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

Sweden

Rodolfo Panerai

Konstantina Polydorou

Topological correlators and surface defects from equivariant cohomology

We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S 4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

Guido Festuccia

Anastasios Gorantis

Lorenzo Ruggeri

Cohomological localization of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 gauge theories with matter

We derive the partition function of an <math><mi>N</mi><mo>=</mo><mn>2</mn></math> chiral multiplet on topologically twisted <math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math>. The chiral multiplet is coupled to a background vector multiplet encoding a real mass deformation. We consider an <math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math> metric containing two parameters: one is the <math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math> radius, while the other gives a fugacity q for the angular momentum on <math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math>. The computation is carried out by means of supersymmetric localization, which provides a finite answer written in terms of q-Pochammer symbols and multiple Zeta functions. Especially, the partition function of normalizable fields reproduces three-dimensional holomorphic blocks.

Supersymmetric localization of refined chiral multiplets on topologically twisted ×

We consider 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry transformations. Our results represent the natural elliptic lifts of the lower dimensional analogs as well as a field theoretic derivation of the conjectured 4d holomorphic blocks, from which partition functions of compact spaces with diverse topology can be recovered through gluing. We also analyze the different boundary conditions which can naturally be imposed on the chiral multiplets, which turn out to be either Dirichlet or Robin-like. We show that different boundary conditions are related to each other by coupling the bulk to 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 degrees of freedom on the boundary three-torus, for which we derive explicit 1-loop determinants.

Switzerland

Pietro Longhi

Germany

Fabrizio Nieri

Localization of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 theories on 𝔻2 × 𝕋2

We introduce bi-fermion fishnet theories, a class of models describing integrable sectors of four-dimensional gauge theories with non-maximal supersymmetry. Bi-fermion theories are characterized by a single complex scalar field and two Weyl fermions interacting only via chiral Yukawa couplings. The latter generate oriented Feynman diagrams forming hexagonal lattices, whose fishnet structure signals an underlying integrability that we exploit to compute anomalous dimensions of BMN-vacuum operators. Furthermore, we investigate Lunin-Maldacena deformations of <math><mi>N</mi><mo>=</mo><mn>2</mn></math> superconformal field theories with deformation parameter γ and prove that bi-fermion models emerge in the limit of large imaginary γ and vanishing 't Hooft coupling g, with <math><mi>g</mi><mspace width="0.2em"></mspace><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mi>γ</mi></mrow></msup></math> fixed. Finally, we explicitly find non-trivial conformal fixed points and compute the scaling dimensions of operators for any γ and in presence of double-trace deformations.

Michelangelo Preti

Integrable fishnet from -deformed Quivers

We find the Yangian symmetry underlying the integrability of type IIB superstrings on <math><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math> with mixed Ramond–Ramond and Neveu–Schwarz–Neveu–Schwarz flux. The abstract commutation relations of the Yangian are formulated via RTT realisation, while its matrix realisation is in an evaluation representation depending on the quantised coefficient of the Wess–Zumino term. The construction naturally encodes a secret symmetry of the worldsheet scattering matrix whose generators map different Yangian levels to each other. We show that in the large effective string tension limit the Yangian becomes a deformation of a unitary loop algebra and we derive its universal classical r-matrix.

Yangian symmetry of string theory on AdS × × × With Mixed 3-form Flux

We verify the self-duality of Green-Schwarz supercoset sigma models on AdS d × S d backgrounds ( d = 2 , 3 , 5) under combined bosonic and fermionic T-dualities without gauge fixing kappa symmetry. We also prove this property for superstrings on AdS d × S d × S d ( d = 2 , 3) described by supercoset sigma models with the isometries governed by the exceptional Lie supergroups D (2 , 1; α ) ( d = 2) and D (2 , 1; α ) × D (2 , 1; α ) ( d = 3), which requires an additional T-dualisation along one of the spheres. Then, by taking into account the contribution of non-supercoset fermionic modes (up to the second order), we provide evidence for the T-self-duality of the complete type IIA and IIB Green-Schwarz superstring theory on AdS d × S d × T 10−2 d ( d = 2 , 3) backgrounds with Ramond-Ramond fluxes. Finally, applying the Buscher-like rules to T-dualising supergravity fields, we prove the T-self-duality of the whole class of the AdS d × S d × M 10−2 d superbackgrounds with Ramond-Ramond fluxes in the context of supergravity.

South Africa

Michael Abbott

Jeff Murugan

Silvia Penati

Dmitri Sorokin

Per Sundin

Justine Tarrant

Martin Wolf

Linus Wulff

T-duality of Green-Schwarz superstrings on AdS d × S d × M 10−2 d

We derive the exact S-matrix for the scattering of particular representations of the centrally-extended p s u 1 | 1 2 $$ \mathfrak{p}\mathfrak{s}\mathfrak{u}{\left(1\Big|1\right)}^2 $$ Lie superalgebra, conjectured to be related to the massive modes of the light-cone gauge string theory on AdS 2 × S 2 × T 6 . The S-matrix consists of two copies of a centrally-extended p s u 1 | 1 $$ \mathfrak{p}\mathfrak{s}\mathfrak{u}\left(1\Big|1\right) $$ invariant S-matrix and is in agreement with the tree-level result following from perturbation theory. Although the overall factor is left unfixed, the constraints following from crossing symmetry and unitarity are given. The scattering involves long representations of the symmetry algebra, and the relevant representation theory is studied in detail. We also discuss Yangian symmetry and find it has a standard form for a particular limit of the aforementioned representations. This has a natural interpretation as the massless limit, and we investigate the corresponding limits of the massive S-matrix. Under the assumption that the massless modes of the light-cone gauge string theory transform in these limiting representations, the resulting S-matrices would provide the building blocks for the full S-matrix. Finally, some brief comments are given on the Bethe ansatz.

Ben Hoare

Alessandro Torrielli

Integrable S-matrices, massive and massless modes and the AdS 2 × S 2 superstring